2010/03/10 by Mladen Savov, Savov, Mladen, Matthias Winkel +1
Mathematics · Physics and Astronomy · #60G51 #Advanced Thermodynamics and Statistical Mechanics #FOS: Mathematics #Probability (math.PR) #Quantum Mechanics and Applications #advanced mathematical theories #math.PR #msc:60G51
paper · pdf · doi:10.48550/arxiv.1003.2122
12 pages
arxiv created 2010/03/10 · openalex publication_date 2010/03/10 · arxiv updated 2010/03/11 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
This article is about right inverses of Levy processes as first introduced by Evans in the symmetric case and later studied systematically by the present authors and their co-authors. Here we add to the existing fluctuation theory an explicit description of the excursion measure away from the (minimal) right inverse. This description unifies known formulas in the case of a positive Gaussian coefficient and in the bounded variation case. While these known formulas relate to excursions away from a point starting negative continuously, and excursions started by a jump, the present description is in terms of excursions away from the supremum continued up to a return time. In the unbounded variation case with zero Gaussian coefficient previously excluded, excursions start negative continuously, but the excursion measures away from the right inverse and away from a point are mutually singular. We also provide a new construction and a new formula for the Laplace exponent of the minimal right inverse.